Pore Analysis

Porous structures are present in a wide range of natural and engineered materials. Their geometry, connectivity, and size distribution strongly influence mechanical, thermal, chemical, and transport properties. Pore analysis plays a central role in materials science, geosciences, energy storage, filtration, catalysis, manufacturing engineering and many other application areas.

This article provides an overview of what pores are, why pore analysis matters, how pores are classified and measured, and how modern image-based modeling and simulation tools, such as GeoDict, enable advanced pore characterization beyond classical measurements.

A pore is a void space within a solid material. Depending on the context, pores may also be referred to as voids, pore spaces, or porosity. These terms are often used synonymously, although porosity typically describes the total volume fraction of all pores relative to the total sample volume.

The precise naming and description of a pore depends on the material system and application, some examples are:

• Manufactured materials with unintentional pores
  Pores may form due to trapped gases, shrinkage, or process instabilities during the manufacturing process, such as in molding, casting, or sintering.
  These pores can be classified as defects and often act as weak points, reducing mechanical strength and fatigue resistance. In industrial quality control, excessive porosity may lead to part rejection.
• Natural porous structures
  In rocks and sediments, pore space controls fluid storage and transport, directly affecting permeability and flow velocity in geological formations. This is important in the oil and gas industry, and pore network models are often used to simplify the description of the connected pore spaces in such rocks. Pore throats are defined as the narrow connections between large, connected pore spaces in these systems, and are important to characterize as they play a crucial role in the transport properties.
• Intentionally designed porous materials
  Many engineered materials are designed to be porous by intent, for example:
  • filtration and membrane materials
  • catalysts and catalyst supports
  • heat exchangers
  • airflow and fluid transport components
• Depending on the manufacturing method, these pore structures may be stochastic or highly ordered.

Pores can form through different mechanisms:

• Primary vs. secondary pores
  Commonly used in geosciences:
  • Primary pores form during deposition
  • Secondary pores form later due to dissolution, compaction, or diagenetic processes
• Manufacturing-related unintentional pores
  • gas entrapment
  • shrinkage during solidification
  • incomplete sintering
• Designed porosity
  Structures intentionally engineered to exhibit specific pore sizes, shapes, and connectivity, such as honeycomb structures or catalyst supports (e.g. in automotive catalytic converters).

The pore structure of a material directly determines key physical and functional properties such as permeability, strength, storage capacity, and transport behavior. Some examples are given below.

• Manufacturing and production
  Pores act as stress concentrators and can cause premature failure under mechanical loading. In some industries such as in aerospace, this risk is unacceptable and manufacturers must ensure porosity is kept to an absolute minimum. Excessive porosity detected by non-destructive test (NDT) methods can often result in scrapped parts.
• Energy storage (batteries and supercapacitors)
  Porosity controls ion transport, electrolyte accessibility, and overall electrochemical performance.
• Biomedical applications
  In tissue scaffolds and drug delivery systems, pore size and connectivity influence:
  • cell migration
  • nutrient and fluid transport
  • release kinetics of active substances
• Construction materials
  Porosity affects:
  • mechanical strength
  • thermal conductivity
  • moisture transport and durability
• Rocks and geosciences
  Pore connectivity determines permeability, influencing oil, gas, and fluid storage and migration in subsurface reservoirs.
• Catalysts
  A porous structure provides a high surface-to-volume ratio, enabling efficient fluid–surface contact and improved catalytic reaction rates.

Pores are commonly categorized by size ranges, typically based on the mean pore diameter. The exact definitions vary by field and application, but commonly used size-based namings include:

• Nanopores
• Micropores
• Mesopores
• Macropores

The classification generally reflects the measurement scale rather than a strict universal definition. For example, a pore with a diameter of approximately 10 µm may be considered a micropore in certain engineering contexts.

Beyond size, pores are often classified by their connectivity and functionality:

• Open vs. closed pores
  Pores connected to the surface (or outside) of the part are classified as “open”, while pores fully enclosed and unconnected to the surface are classified as “closed”.
• Effective vs. non-effective porosity
  Common in reservoir engineering, where only connected pores contribute to flow and transport.

A wide range of experimental techniques exists for pore characterization. Each method provides different information and comes with specific advantages and limitations.

• Materialography / Metallography
  • 2D section-based analysis of pore morphology, often using an optical microscope.
• Micro-CT (X-ray computed tomography)
  • Non-destructive 3D imaging of pore structure and connectivity.
• SEM and FIB-SEM
  • High-resolution surface and volume imaging at micro- to nanoscale using scanning electron microscope.
• Porosimetry
  • The volume of a non-wetting fluid forced into the medium is calculated
  • Gas or liquid-based methods, mercury intrusion porosimetry is widely used
  • Used for catalysts, pharmaceuticals, construction materials and rocks
• Adsorption techniques
  • Quantify pore volume, surface area, and pore size distribution by measuring gas uptake at varying pressures 
  • Commonly used for nanoporous materials 
• Capillary Flow Porometry
  • Uses liquid expulsion calculations
  • Non-destructive measurement of pore throat sizes, especially in membranes and filtration media
• Thermoporometry / Cryoporometry
  • Thermal methods based on melting and freezing behavior in confined pores.
• NMR in porous media
  • Measures porosity by detecting the total volume of Hydrogen-rich fluids like water and oil in pore spaces 
  • Provides information on pore size distribution, fluid saturation and wettability
• Imbibition and evaporation methods
  • Simpler or complementary approaches reflecting connectivity and permeability.

* Note: Pore size ranges depend on material, instrument configuration, and experimental setup. 

Quantitative pore analysis relies on a range of geometrical and topological metrics, including:

• Total pore volume
• Porosity (pore volume fraction)
• Pore size distribution
• Specific surface area
• Open vs. closed porosity
• Pore connectivity
• Pore throat sizes

More advanced descriptors include:

• inscribed and circumscribed sphere diameters
• minimum and maximum inscribed spheres
• Feret diameters and longest axes
• pore network models
• shape factors and sphericity

These metrics can be defined differently in 2D and 3D, which has a strong impact on interpretation.

Modern pore analysis increasingly relies on image-based methods, particularly for Micro-CT and microscopy data.

The core concept is the segmentation of pore space from solid material, followed by quantitative analysis. Segmentation of porosity often makes use of thresholding-based methods (such as Otsu’s method) based on the greyvalue distribution of the full image, to classify or segment pixels or voxels into pore space.

• 2D analysis has some advantages:
  • is fast and relatively simple
  • provides quantitative porosity information
  • and is easy to interpret and visualize
• 2D analysis has some disadvantages:
  • the 2D section analyzed may not be representative of the full volume
  • pore sizes are often underestimated, e.g. image a sphere with multiple sections taken through it, most will have smaller diameter in 2D than the central slice
  • misinterpretation of irregular shapes pores, e.g. imagine a curved (“banana-shaped”) pore, in some orientations in 2D it will seem to be two separate pores but is in fact one
• 3D analysis captures true pore geometry and connectivity and is therefore essential for transport-related properties. The disadvantage is that high quality imaging is more complex and may be more time consuming or expensive.

There are some challenges involving pore segmentation in images, including the following:

• Noisy images can result in lots of “false positive” segmentations of pores
• Image brightness variations or poor contrast can make a global threshold unsuitable
• Image artifacts can result in false segmentations or missed pores
• Small pores are subject to partial volume effect, causing an increase in their brightness, resulting in under-segmentation or missed segmentations

Noise issues are usually solved by applying de-noising image filtering (see image processing). Brightness variations, poor contrast or image artifacts can lead to unsuccessful segmentation and recommending improved image acquisition. 

However, there are fundamental limits of the digital pore analysis method when it comes to small pores. For example, if your pixel or voxel size is 10 µm, this does not mean that a pore can be quantified with this size. 

If a pore exists in the material, its image needs to have a few pixels across its width to properly identify it and overcome the partial volume effect. Ideally, more than 10 pixels to clearly see a pore space is recommended when working with simulations. 

However, for less demanding materials characterization and non-destructive testing needs, a common rule of thumb is that a pore must span at least three voxels in one dimension to be reliably detected. 

Typically, digital pore analysis excludes those with smaller dimensions. It is therefore important to quantify and record the range of pore sizes measured, since smaller pores can still exist in the material.

Connectivity depends on how voxel neighbors are defined:

• face-connected
• edge-connected
• corner-connected

The connectivity definitions can be used to define if neighbouring pore spaces are connected or not, depending on if two voxels, one of each pore, are adjacent to each other face-to-face, only by edges touching, or only by corners touching. 

Watershed algorithms are commonly used to separate connected pore regions into individual pores for statistical analysis. This procedure is useful when analyzing large open connected pore spaces.

Modern pore analysis does not stop at measuring pore size distributions or porosity. Once the pore space is available as a 3D digital representation, it becomes possible to simulate physical processes directly within the pore structure. This enables quantitative predictions of material behavior that are difficult or impossible to obtain from experiments alone.

Classical pore metrics describe what the structure looks like.
Simulation-based analysis answers what the structure does.

By numerically solving physical equations inside the real pore geometry, one can link microstructure directly to functional material properties, such as transport, flow, or effective material coefficients.

One of the most common applications of simulation-based pore analysis is the prediction of transport properties, including:

• Permeability
  Simulation of fluid flow through the connected pore space to quantify permeability in different directions.
• Tortuosity
  Calculation of effective transport path lengths for fluids, ions, or gases through complex pore networks.
• Diffusion and conduction
  Modeling of diffusive transport (e.g. ions, gases) or electrical and thermal conduction through porous structures.

These simulations are directly based on the true 3D pore geometry, capturing effects of:

• pore connectivity
• bottlenecks and pore throats
• anisotropy
• dead-end pores

For large or highly resolved datasets, pore space can be converted into simplified pore network models:

• The continuous pore space is reduced to a network of pores (nodes) and throats (links)
• Also called ball-and-stick models
• Network models preserve essential topological information while enabling faster simulations

This approach is widely used in:

• filtration and membrane analysis
• battery electrodes
• rocks and reservoir engineering

Pore network models enable efficient prediction of flow, diffusion, and multiphase transport while remaining physically interpretable.

Simulation-based pore analysis is not limited to single physical effects. Depending on the application, multiple coupled phenomena can be modeled, such as:

• Fluid flow coupled with transport
• Electrochemical transport in battery electrodes
• Thermal transport in porous heat exchangers
• Reactive transport in catalysts

This allows investigation of structure–property relationships, for example:

• how pore size gradients affect performance
• how clogging or partial saturation changes transport
• how anisotropic pore structures influence effective properties

Many real materials exhibit pores across multiple length scales, from nanometers to hundreds of micrometers. Simulation-based approaches allow:

• combination of high-resolution data for small pores with coarser data for large-scale structure
• upscaling of transport properties from pore scale to component scale

This is particularly relevant for:

• battery materials
• filtration media
• catalyst supports

Simulation-based pore analysis transforms pore characterization into a form of virtual material testing:

• properties can be evaluated without destroying samples
• design variants can be compared digitally
• sensitivity studies can be performed systematically

This closes the gap between experimental imaging, quantitative analysis, and predictive material modeling.

GeoDict is a comprehensive digital material characterization and simulation platform developed by Math2Market. It enables image-based pore analysis combined with physics-based simulations, allowing pore geometry to be directly linked to functional material properties.

For many applications, pore analysis starts with a standardized image-based workflow that quantifies pore geometry and statistics from 3D data.

Using the PoroDict module, users can perform the following steps:

1. Import of 3D image data
   Typical sources include Micro-CT or FIB-SEM image stacks.
2. Segmentation of pore and solid phases
   Binary or multi-phase segmentation separates pore space from the solid matrix.
3. Identification and analysis of individual pores
   For each pore, PoroDict provides statistical descriptors such as:
   • pore diameter
   • pore volume
   • surface area and perimeter
   • sphericity and shape factors
   • aspect ratio
   • orientation
   • open vs. closed pore classification
4. Visualization of pore space and analysis results
   Pores can be visualized individually or color-coded by size, volume, connectivity, or other metrics.

A commonly used example is the “Identify Pores” workflow in PoroDict, which detects individual pores and generates detailed statistical reports and visualizations.

Beyond basic pore statistics, GeoDict supports advanced pore-based simulations that directly operate on 3D microstructures. These workflows are used when pore structure must be linked to transport, flow, or effective material behavior.

Using segmented pore geometries, GeoDict enables direct calculation of:

• Permeability, by simulating fluid flow through the connected pore space
• Tortuosity, based on geometric paths or physics-based transport simulations

These analyses are commonly applied in:

• digital rock physics
• battery electrode analysis
• filtration and membrane materials

In many applications, pore characterization is combined with flow simulation to obtain effective transport properties from real microstructures.

A typical example is Digital Routine Core Analysis, where GeoDict workflows combine:

• pore identification and porosity analysis (PoroDict)
• flow simulation through the pore space
• automated reporting of permeability and related metrics

This workflow is widely used in digital rock and core analysis.

By combining 3D image analysis with physics-based simulations, GeoDict enables pore analysis to move beyond descriptive metrics toward predictive digital material testing. This allows material behavior to be evaluated virtually, reducing experimental effort and supporting data-driven material development.

Are you interested in exploring the digital material development with GeoDict? Math2Market offers a free trial license that allows you to test the software’s capabilities and experience its workflow first-hand.

With the trial version, you can:

• Import and visualize 3D structures,
• Carry out pore analyses,
• Explore modules such as PoroDict, and
• Evaluate how GeoDict supports your research or product development tasks.

To request your trial license or learn more about GeoDict’s features, visit our page

GeoDict Trial License